Today, many forms of information are sent from sources, such as television content providers, to receivers, such as televisions in people's homes. An example of such information is digital television (DTV) information. Transmitting digital information typically involves converting the digital information to an analog signal, modulating an RF (radio frequency) carrier frequency's amplitude and/or phase using the analog signal, and sending the modulated signal over a propagation medium, such as air, towards a receiver.
Referring to FIG. 1, a communications system 1 includes a transmitter 2 and a receiver 4. The transmitter 2 and the receiver 4 have respective antennas 6 and 8, here shown externally to the transmitter 2 and the receiver 4, although the antennas 6 and 8 may be considered to be parts of the transmitter 2 and the receiver 4. The transmitter 2 is configured to send information over the propagation medium to the receiver 4 (e.g., as signals 14, 16, and 18). Transmitting information over the propagation medium introduces signal distortion caused by noise (e.g., static), strength variations (fading), phase shift variations, Doppler spreading, Doppler fading, multiple path delays, etc. Multiple path delays result from the transmitted signals taking different paths between the transmitter and receiver through the propagation medium, e.g., due to reflections off a building 10 and/or being relayed through a repeater station 12. Different paths of a transmitted signal p(t) (e.g., the signals 14, 16, and 18) result in different gains and different delay times that can cause time-delayed copies of the signal p(t) to arrive at different times at the receiver 4 (like an echo) compared to the directly-transmitted signal 16. The received signal r(t) is a combination of the directly-transmitted signal and/or the replicas, if any. Multi-path distortion results in intersymbol interference (ISI) in which weighted contributions of other symbols are added to the current symbol, and/or interchannel interference in which separate sub-carriers interfere with each other. Noise and/or interference in the signal r(t) can also come from other sources such as the transmitter. These effects can cause errors in the transfer and/or interpretation of information from the transmitter 2 to the receiver 4. When a bit error rate (BER) of a system exceeds a threshold and overcomes the error tolerance of the system, the system fails.
Orthogonal Frequency Division Multiplexing (OFDM) can be used to transmit multiple DTV signals over the propagation medium. OFDM systems transmit a signal, such as a television signal, in parallel over one or more sub-carriers, using one or more time slots in each sub-carrier. Each sub-carrier is located at a different portion of a frequency spectrum used to transmit the DTV signals. The spacing of the sub-carriers is such that each sub-carrier's frequency is orthogonal to each of the other sub-carriers' frequencies (e.g., frequency spacing of the sub-carriers is substantially equal to the inverse of an OFDM symbol duration). The orthogonality of the sub-carrier frequencies provides a higher resistance to RF interference and multi-path distortion than when non-orthogonal frequencies are used as sub-carriers. Each sub-carrier includes, for example, data symbols, pilot symbols, and/or Transmission Parameter Signals (TPS) symbols, which are a special type of data symbol. The pilot symbols are predetermined known signals used to help a receiver estimate transmission channels.
Once an OFDM signal (e.g., r(t)) is received by the receiver 4, channel estimation is used to cancel the effects of the distortion on the transmitted signal (e.g., p(t)). For example, because r(t) is a linear combination of the signals 14, 16, and 18, a specific mathematical function (i.e., a transfer function) can describe the relation of p(t) to r(t). Once the transfer function of the propagation medium is known, a filter that is the inverse of the transfer function of the propagation medium can be used to reduce the effects of the distortion introduced by the propagation medium. Because the propagation medium is constantly changing (e.g., objects that create multi-path errors can move, weather can change, noise levels can change, etc.), the transfer function of any given propagation medium is also constantly changing. When the propagation medium is changing slowly, r(t) becomes a “slow fading” transmission channel, which can affect the estimation process. “Long channels” occur when the propagation medium has a long delay spread. For example, if the distance that the signal 18 travels to reach the receiver 4 is sufficiently long compared to the signal 16, a symbol in the signal 18 may arrive at the receiver 4 after the same symbol arrives via the signal 16, thus creating ISI.